Modern Portfolio Theory has a strong emphasis on reducing risk, which can also be described as lowering volatility (the degree to which an investment goes up or down). By placing investments into a portfolio that are not strongly positively correlated, this can reduce the over level of risks. For example the US Stock-market and Gold could considered to be negatively correlated, i.e. in economic turmoil gold often raises in price, whilst stocks go down. These two assets would be beneficial together in a portfolio as they hep reduce the impact of economic risk.
It is assumed that investors want to maximise returns, and minimise risk. As reducing risk often reduces the potential return, there is a combination of risk/return which is deemed optimal. This optimal level is called the efficient frontier.
The efficient frontier is a theoretical model that illustrates where both the minisation of risk and the maximisation of return are being achieved, when comparing a group of different portfolios.
The chart below plots the performance of a range of investment portfolios. Each dot represents an investment portfolio and is plotted in accordance to it’s overall risk and return. The efficient frontier is the curved green line. Anything below this line is giving less return for the same level of risk, hence it is not optimal. anything on the curved line (the efficient frontier) is giving the maximum return for that level of risk.
It is essentially a comparison tool that ensures the optimal performing portfolio is chosen for a given risk level.
This video from Udacity provides a useful overview of the theory behind finding the optimum portfolio, with the efficient frontier.
The video below takes a more technical view of correlation, risk, return, and optimisation. It essentially covers the same principles as discussed here, by going into more detail in regards to the calculations behind obtaining a maximum risk/return relationship.